Authors: Abay Molla Kassa Semu Mitiku Kassa
Publish Date: 2015/07/23
Volume: 64, Issue: 4, Pages: 745-764
Abstract
In this paper we develop a general but smooth global optimization strategy for nonlinear multilevel programming problems with polyhedral constraints At each decision level successive convex relaxations are applied over the nonconvex terms in combination with a multiparametric programming approach The proposed algorithm reaches the approximate global optimum in a finite number of steps through the successive subdivision of the optimization variables that contribute to the nonconvexity of the problem and partitioning of the parameter space The method is implemented and tested for a variety of bilevel trilevel and fifth level problems which have nonconvexity formulation at their inner levelsThis work is in part supported by the Swedish International Science Program ISP through the project at the Department of Mathematics Addis Ababa University The authors also would like to thank the anonymous referees from whom we received valuable comments and suggestions to improve the earlier version of the manuscript
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